Magnetohydrodynamics in narrow fluidic channels in presence of spatially non-uniform magnetic fields: framework for combined magnetohydrodynamic and magnetophoretic particle transport

In this paper, we bring out the implications of a spatially varying magnetic field towards combined magnetohydrodynamic-magnetophoretic transport in narrow fluidic confinements. We first present a generic framework for describing the flow field that is generated under the combined influences of a driving pressure gradient, an axial electric field, and a spatially varying transverse magnetic field. As a demonstrative example, we derive analytical solutions for the flow field, based on a plausible choice of the mathematical form of the nature of spatial variation of the magnetic field. Proceeding further ahead, we also address the magnetophoretic motion of particles, subjected to such spatially varying magnetic fields. We depict the trajectories of representative spherical particles in the flow-field, as a combined consequence of the magnetohydrodynamic and magnetophoretic forcing mechanisms. We also demonstrate that such combined magnetophoretic and magnetohydrodynamic transport can be employed as a novel technique to separate particles based on sizes and electromagnetic properties.